Chapter 7 Separation of Particles from a Gas

Transcription

1 Chapter 7 Separation of Particles from a Gas For either gas cleaning (removal of dusts) or recovery of particulate products Separation Mechanisms Sedimentation : Settling chamber, centrifuge Migration of charged particle in an electric field : Electrostatic precipitator Inertial deposition : Cyclone, scrubber, filters, inertial impactor Brownian diffusion : Diffusion batteries * Filters Figure Gas Cyclones Figure Flow Characteristics

2 Rotational flow in the forced vortex in the cyclone body radial pressure gradient Resistance coefficient: Euler number where v = Eu 4q πd 2 ~ Δ p ρ f v 2 /2 pressure force inert force * Economy of the collectors Based on $/(1000 m 3 cleaned gas /h) annualized capital cost + operating cost* : * Power requirement Q Δp, [W] where Δp = f(l,v,ρ f,μ) Eu = f(re p ) ~ constant By dimensional analysis for a given cyclone, independent of D 7.3 Efficiency of Separation (1) Total Efficiency and Grade Efficiency Total mass balance M= M f +M c where M : total mass flow rate M c : mass flow rate discharged from the solid exit orifice (coarse product) M f : solid mass flow rate leaving with the gas (fine product) Component mass balance M df = M df f f +M df c c (*) where df, df c, df f : differential frequency size

3 distribution s by mass for the feed, coarse product and fine product Total efficiency, E T Grade efficiency, G(x) E T = M c M G(x)= mass of solids of size x in coarse product mass of solids of size x in feed From (*) G(x)= M c df c M df df c = E T df In cumulative form df = E df c T +(1-E T) df f F=E T F c +(1-E T )F f (2) Simple Theoretical Analysis for Gas Cyclone Separator Figure 7.3 At equilibrium orbit, r 3πxμU r = π x 3 6 (ρ p - ρ f ) U 2 θ r F D F C - F B where U θ r 1/2 = constant for confined vortex = U θr R 1/2 U r r=constant for radially inward flow = U R R x 2 = 18 μ ρ p -ρ f U R U 2 θr r

4 where r : the radius of the equilibrium orbit (displacement) for a particle of diameter x For all the particles to be collected, r R x 2 crit = 18 μ ρ p -ρ f U R U 2 θr R where x crit : critical(minimum) diameter of the particles to be collected or If x > x crit, G(x)=1 and otherwise, G(x)=0 (3) Cyclone Grade Efficiency in Practice Ideal grade efficiency curve Figure 7.4 Actual grade efficiency curve, "S"-shaped : distorted due to velocity fluctuation and particle-particle interaction * x 50 and St 50 in stead of x crit and St crit where cut size, x 50 x at G(x)= Scale-up of Cyclone Dimensional analysis for G(x) G(d p )=f(x,ρ p,ρ f,l,v) G(x)=f(St,Re,x/L) where L : characteristic length of the separator U : characteristic velocity of the particle in the separator St ρ px 2 U 18μL and Re ρ f UL μ From both theoretical and actual analysis for given cyclone,

5 St 50 ( ρ px 2 50U 18μD ) ~ constant x 50 μd 3 /ρ p Q Eu ( Δ p ρ f U 2 /2 ) constant Δp Q 2 /D 4 π independent U=Q/ 4 D 2 of Re Standard Cyclone Designs - dimension Figure High efficiency Stairmand cyclone: St 50 = and Eu = High flow rate Stairmand cyclone St 50 = and Eu =46 Grade efficiency Figure 7.6 G(x)= ( x x 50 ) 2 [ 1+ ( x x 50 ) 2 ] for the geometry shown in p Range of operation Figure 7.7 : optimum operation somewhere between A and B cf. Reentrainment 7.6 Some Practical Design and Operation Details High dust loading ( >~5g/m 3 ) high separation efficiency For well-designed cyclone due to agglomeration Eu= 12 Stk 50

6 Abrasion: gas inlet and particle outlet lined with rubber, refractory lining or the materials Attrition: large particles with recirculation system Blockages: overloading, mechanical defects and water condensation Discharge hoppers(vortex breaker and stepped cone) and diplegs (internal cyclone in fluidized bed) Cyclones in series: increasing recovery N cyclones in parallel For large gas flow rate Q Q/N Worked Example 7.1 Worked Example S Aerosol Impactor U D j Particle trajectory S Streamline In general, for inertial motion of particles, G(x)=f ( Stk(x),Re, S D j ) For given geometry ( S/D j ) where Stk(x)= τ(x)u D 0.5 = f(stk 50,Re) Stk 50 = f 1 (Re)

7 From numerical and/or experimental analysis Stk(x): almost independent of Re Or for 500 < Re < 3000 and S/D > 1.5 For circular nozzle, Stk 50 = 0.22 For rectangular nozzle, Stk 50 = μDStk x 50 = [ 50 ρ p UC c ] 1/2 작은입자를잡으려면노즐입경을줄이고, 유속을올리는방법과 C c 를올 리는방법이있다. C c 를올리려면어떻게해야하나? * Cascade impactor Particleladen air Stage 1 Stage 2 Stage 3 To filter - Measurement of particle size distribution - Classification of particles

8 Summary of Particulate Collection Minimum particle size Efficiency (%) (mass Advantages Device (μm) basis) Gravitational >50 <50 Low-pressure loss settler Simplicity of design and maintenance Cyclone Simplicity of design and maintenance Little floor space required Dry continuous disposal of collected dusts Low-to-moderate pressure loss Handles large particles Handles high dust loadings Temperature independent Wet collectors Simultaneous gas absorption and Spray towers >10 <80 particle removal Cyclonic >2.5 <80 Ability to cool and clean hightemperature, Impingement >2.5 <80 moisture-laden Venturi >0.5 <99 gases Corrosive gases and mists can be recovered and neutralized Reduced dust explosion risk Efficiency can be varied Electrostatic < % efficiency obtainable precipitator Very small particles can be collected Particles may be collected wet or dry Pressure drops and power requirements are small compared with other high-efficiency collectors Maintenance is nominal unless corrosive or adhesive materials are handled Few moving parts Can be operated at high temperatures(573 to 723 K) Fabric <1 >99 Dry collection possible filtration Decrease of performance is noticeable Collection of small particles possible High efficiencies possible Disadvantages Much space required Low collection efficiency Much head room required Low collection efficiency of small particles Sensitive to variable dust loadings and flow rates Corrosion, erosion problems Added cost of wastewater treatment and reclamation Low efficiency on submicron particles Contamination of effluent stream by liquid entrainment Freezing problems in cold weather Reduction in buoyancy and plume rise Water vapor contributes to visible plume under some atmospheric conditions Relatively high initial cost Precipitators are sensitive to variable dust loadings or flow rates Resistivity causes some material to be economically uncollectable Precautions are required to safeguard personnel from high voltage Collection efficiencies can deteriorate gradually and imperceptibly Sensitivity to filtering velocity High-temperature gases must be cooled Affected by relative humidity (condensation) Susceptibility of fabric to chemical attack